After adding a question, the OP (original poster of the question) has a grace period during which he or she is permitted to delete the question; this grace period ends when a certain level of activity on the page has occurred. This policy is consistent with Quora's philosophy that questions belong to the community and OPs do not have ownership over their questions.
If the question is still within this grace period, the OP can delete it by visiting their question page, clicking on the "…" link below the question title, then selecting the "Delete" option. If this option isn’t present, it means the question can no longer be deleted by the OP.